Usage
sparse.DDE(fn, data, times, basisvals = NULL, lambda, fd.obj = NULL, more = NULL, weights = NULL, quadrature = NULL, in.meth = "nlminb", out.meth = "nls", control.in = list(), control.out = list(), eps = 1e-06, active = NULL, posproc = FALSE, poslik = FALSE, names = NULL, sparse = FALSE, discrete = FALSE, basisvals0 = NULL, coefs0 = NULL, nbeta, ndelay, tau, nnls.res)
Arguments
fn
A named list of functions giving the righthand side of a delay differential equation. The functions should have arguments
- times
- he times at which the righthand side is being evaluated.
- x
- The state values at those times.
- p
- Parameters to be entered in the system.
- more
- A list object containing additional inputs to
fn, The distributed delay state are passed into derivative calculation as more$y. The list of functions should contain the elements:
- fn
- Function to calculate the right hand sid.
- dfdx
- Function to calculate the derivative of each right-hand function with respect to the states.
- dfdp
- calculates the derivative of therighthand side function with respect to parameters.
- d2fdx2
- Function to calculate the second derivatives with respect to states.
- d2fdxdp
- Function to calculate the cross derivatives of each right-hand function with respect to state and parameters.
- dfdx.d
- Function to calculate the the derivative of each righthand function with respect to the delayed states.
- d2fdx.ddp
- Function to calculate the cross derivatives of each righthand function with respect to the delayed states and parameters.
- d2fdxdx.d
- Function to calculate the cross derivatives of each right-hand function with respect to the state and the delayed states.
- d2fdx.d2
- Function to calculate the second derivatives of the right-hand function with respect to the delayed states.
data
Matrix of observed data values.
times
Vector observation times for the data.
basisvals
Values of the collocation basis to be used. This should be a basis object from the fda package.
lambda
Penalty value trading off fidelity to data with fidelity to dif- ferential equations.
fd.obj
A functional data object; if this is non-null, coefs and basisvals is extracted from here.
more
An object specifying additional arguments to fn.
weights
Weights for weighted estimation.
quadrature
Quadrature points, should contain two elements (if not NULL)
- qpts
- sQuadrature points; defaults to midpoints between knots
- qwts
- Quadrature weights; defaults to normalizing by the length of qpts.
in.meth
Inner optimization function currently one of 'nlminb', 'optim', or 'trustOptim'.
out.meth
Outer optimization selection function to be used, depending on the type of method.
- "penalized"
- Uses LASSO method from
penalized package. - "addaptive"
- Positive addaptive lasso using lars algorithm.
- "lars"
- Positive lasso using lars algorithm.
control.in
Control object for inner optimization function.
control.out
Control object for outer optimization function.
eps
Finite differencing step size, if needed.
active
Incides indicating which parameters of pars should be estimated; defaults to all of them.
posproc
Should the state vector be constrained to be positive? If this is the case, the state is represented by an exponentiated basis expansion in the proc object.
poslik
Should the state be exponentiated before being compared to the data? When the state is represented on the log scale (posproc=TRUE), this is an alternative to taking the log of the data.
names
The names of the state variables if not given by the column names of coefs.
sparse
Should sparse matrices be used for basis values? This option can save memory when using 'trust' optimization method.
discrete
Is it a discrete process?
basisvals0
Values of the collocation basis to be used for the history part of the data. This should be a basis object from the fda package.
coefs0
Vector giving the estimate of the coefficients in the spline for the history part of the data.
nbeta
The number of lags for the delay.
ndelay
A vector inidicating which state process has a delay term.